On the universal constant in the Katz-Petrov and Osipov inequalities

Victor Korolev; Sergey Popov

Discussiones Mathematicae Probability and Statistics (2011)

  • Volume: 31, Issue: 1-2, page 29-39
  • ISSN: 1509-9423

Abstract

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Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.

How to cite

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Victor Korolev, and Sergey Popov. "On the universal constant in the Katz-Petrov and Osipov inequalities." Discussiones Mathematicae Probability and Statistics 31.1-2 (2011): 29-39. <http://eudml.org/doc/277014>.

@article{VictorKorolev2011,
abstract = {Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.},
author = {Victor Korolev, Sergey Popov},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {central limit theorem; convergence rate estimate; absolute constant; Katz-Petrov inequality; Osipov inequality},
language = {eng},
number = {1-2},
pages = {29-39},
title = {On the universal constant in the Katz-Petrov and Osipov inequalities},
url = {http://eudml.org/doc/277014},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Victor Korolev
AU - Sergey Popov
TI - On the universal constant in the Katz-Petrov and Osipov inequalities
JO - Discussiones Mathematicae Probability and Statistics
PY - 2011
VL - 31
IS - 1-2
SP - 29
EP - 39
AB - Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.
LA - eng
KW - central limit theorem; convergence rate estimate; absolute constant; Katz-Petrov inequality; Osipov inequality
UR - http://eudml.org/doc/277014
ER -

References

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  2. [2] L.H.Y. Chen and Q.M. Shao, A non-uniform Berry-Esseen bound via Stein's method, Probability Theory and Related Fields 120 (2001) 236-254. Zbl0996.60029
  3. [3] W. Hoeffding, The extrema of the expected value of a function of independent random variables, Ann. Math. Statist. 19 (1948) 239-325. 
  4. [4] M. Katz, Note on the Berry-Esseen theorem, Annals of Math. Statist. 39 (4) (1963) 1348-1349. 
  5. [5] V.Yu. Korolev and I.G. Shevtsova, An improvement of the Berry-Esseen inequality with applications to Poisson and mixed Poisson random sums, Scandinavian Actuarial Journal, 2010. Online first: http://www.informaworld.com/10.1080/03461238.2010.485370, 04 June 2010. Zbl1277.60042
  6. [6] J.S. Nefedova and I.G. Shevtsova, On non-uniform estimates of convergence rate in the central limit theorem, Theory Probab. Appl. 56 (2011), to appear. Zbl1245.60030
  7. [7] L.V. Osipov, A refinement of the Lindeberg theorem, Theory Probab. Appl. 11 (2) (1966) 339-342. 
  8. [8] L. Paditz, Bemerkungen zu einer Fehlerabschätzung im zentralen Grenzwertsatz, Wiss. Z. Hochschule für Verkehrswesen Friedrich List 27 (4) (1980) 829-837. 
  9. [9] L. Paditz, On error-estimates in the central limit theorem for generalized linear discounting, Math. Operationsforsch. u. Statist., Ser. Statistics 15 (4) (1984) 601-610. Zbl0553.60030
  10. [10] L. Paditz, Über eine Fehlerabschätzung im zentralen Grenzwertsatz, Wiss. Z. Hochschule für Verkehrswesen Friedrich List Dresden 33 (2) (1986) 399-404. Zbl0606.60031
  11. [11] V.V. Petrov, An estimate of the deviation of the distribution of a sum of independent random variables from the normal law, Soviet Math. Dokl. 160 (5) (1965) 1013-1015. 
  12. [12] V.V. Petrov, Sums of Independent Random Variables (New York, Springer, 1975). 
  13. [13] I.G. Shevtsova, A refinement of the estimates of the rate of convergence in the Lyapunov theorem, Doklady Mathematics 435 (1) (2010) 26-28. 

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